what two numbers when multiplied together equal 120, but when added together equal 26?

Question

johnweldon1993 · Answer

So lets let number 1 = x and number 2 = y

Then

x * y = 120
and
x + y = 26

Can you solve this system of equations?

johnweldon1993 · Answer

So what we're gonna do...is solve that bottom equation for 'x' and then substitute what we find into the top equation...

x + y = 26

we want to solve for 'x' so subtract 'y' from both sides...

x = 26 - y

Since we now know that x = 26 - y...in the first equation we have

x * y = 120

turns into

(26 - y)(y) = 120

Distribute this out...

26y - y^2 = 120

Subtract 120 from both sides...

-y^2 + 26y - 120 = 0

Quadratic...can you solve for the solutions?